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If a and b are integers, ab = 5, and a b > 0, which of the followin

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Bunuel
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If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   16 Mar 2022, 03:45
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If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

I. \(a > -1\)
II. b is odd
III. \(|a|=5\)

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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mpobisetty
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Re: If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   16 Mar 2022, 03:50
Two combinations possible for a and b: (5,-1) or (1,-5).

Hence, option C.
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Re: If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   17 Sep 2023, 04:08
If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

We can make 2 cases to satisfy the prompt
1) a = 1 and b = -5
2) a = 5 and b = -1

Now onto the questions
I. a > -1
as we can see from our breakdown a can be 1 or 5, therefore a > -1 (keep)

II. b = odd
as we can see from our breakdown b can be -5 or -1, which are both odd (keep)

III. |a| = 5
from our breakdown a can be 5, which makes this statement true, but a can also be 1, therefore this one must not be true

Answer C
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RC_xx
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Re: If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   13 Jun 2024, 00:59
nasgmatbag
If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

We can make 2 cases to satisfy the prompt
1) a = 1 and b = -5
2) a = 5 and b = -1

Now onto the questions
I. a > -1
as we can see from our breakdown a can be 1 or 5, therefore a > -1 (keep)

II. b = odd
as we can see from our breakdown b can be -5 or -1, which are both odd (keep)

III. |a| = 5
from our breakdown a can be 5, which makes this statement true, but a can also be 1, therefore this one must not be true

Answer C
­I'm in trubble with this kind of question, I totally agree with your approach, I followed it as well, however I tought if a > -1 a could be 0 then a*b is not -5.

Bunuel

 
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If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   13 Jun 2024, 01:16
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RC_xx
nasgmatbag
If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

We can make 2 cases to satisfy the prompt
1) a = 1 and b = -5
2) a = 5 and b = -1

Now onto the questions
I. a > -1
as we can see from our breakdown a can be 1 or 5, therefore a > -1 (keep)

II. b = odd
as we can see from our breakdown b can be -5 or -1, which are both odd (keep)

III. |a| = 5
from our breakdown a can be 5, which makes this statement true, but a can also be 1, therefore this one must not be true

Answer C
­I'm in trubble with this kind of question, I totally agree with your approach, I followed it as well, however I tought if a > -1 a could be 0 then a*b is not -5.

Bunuel



 
a cannot be 0 precisely because we are told that ab = -5. We are given some conditions, and then are asked which of the following MUST be true. ab = -5, and a - b > 0 implies that a must be a positive number. For ANY positive number, it will be true to say that it is more than -1; however, it does not mean that a can be any number greater than -1.­
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shreysigulati10
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Re: If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   24 Jun 2024, 08:49
I understand the explanation but since the Q claims that a-b> 0, does it not imply that a is larger than b and hence must be 5 and not 1
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Re: If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink] If a and b are integers, ab = 5, and a b > 0, which of the followin   24 Jun 2024, 08:53
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shreysigulati10
If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?

I. \(a > -1\)
II. b is odd
III. \(|a|=5\)

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


I understand the explanation but since the Q claims that a-b> 0, does it not imply that a is larger than b and hence must be 5 and not 1
­a and b are integers, ab = −5, and a − b > 0 implies that we can have the following two cases:

a = 5 and b = -1
a = 1 and b = -5

As you can see, in both cases a > b.­
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Re: If a and b are integers, ab = 5, and a b > 0, which of the followin [#permalink]
24 Jun 2024, 08:53
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